Given that E is the midpoint of AD and BC, which of the following proves that AB∥CD?
HELP ASAP!

Answers

Answer 1

The proof that shows that AB∥CD in the diagram given is:

1. E is the midpoint of AD --> Given

2. [tex]\overline{AE} \cong \overline{ED}[/tex] ---> Definition of midpoint

3. E is the midpoint of BC --> Given

4. [tex]\overline{BE} \cong \overline{EC}[/tex] ---> Definition of midpoint

5. ∠AEB ≅ ∠CED --> Vertical Angles Theorem

6. ΔABE ≅ ΔDCE ---> SAS Congruence Theorem

7. AB∥CD ---> CPCTC Theorem.

The given figure showing ΔABE ≅ ΔDCE is in the image attached below.

We know that:

E is the midpoint of AD. Therefore, AE ≅ ED by the definition of midpoint.

E is the midpoint of BC. Therefore, BE ≅ EC by the definition of midpoint.

∠AEB and ∠CED are vertical angles, therefore, ∠AEB ≅ ∠CED by the vertical angles theorem.

This means that ΔAEB and ΔDEC have:

two pairs of congruent sides - AE ≅ ED and BE ≅ EC

one pair of congruent included side -  ∠AEB ≅ ∠CED

Hence, ΔABE ≅ ΔDCE by the SAS Congruence Theorem.

If both triangles are congruent, it implies that all corresponding sides and angles of ΔAEB will be congruent to that of ΔDEC.

Therefore, AB∥CD by the CPCTC Theorem.

Thus, the proof that shows that AB∥CD in the diagram given is:

1. E is the midpoint of AD --> Given

2. [tex]\overline{AE} \cong \overline{ED}[/tex] ---> Definition of midpoint

3. E is the midpoint of BC --> Given

4. [tex]\overline{BE} \cong \overline{EC}[/tex] ---> Definition of midpoint

5. ∠AEB ≅ ∠CED --> Vertical Angles Theorem

6. ΔABE ≅ ΔDCE ---> SAS Congruence Theorem

7. AB∥CD ---> CPCTC Theorem.

Learn more about the CPCTC Theorem on:

https://brainly.com/question/14706064

Given That E Is The Midpoint Of AD And BC, Which Of The Following Proves That ABCD?HELP ASAP!

Related Questions

This is not urgent, so thank you even if you don’t help.

Answers

Answer:

(1/2) and 9/10

Step-by-step explanation:

[tex]\dfrac{1}{2}+\dfrac{9}{10}=\dfrac{1*5}{2*5}+\dfrac{9}{10}\\\\\\=\dfrac{5}{10}+\dfrac{9}{10}\\\\=\dfrac{14}{10}\\\\=\dfrac{7}{5}\\\\=1\dfrac{2}{5}[/tex]

Factor completely:

–abc –5ac –4ab –20a

Answers

Answer:

[tex]-a(b+5)(c+4)[/tex]

Step-by-step explanation:

[tex]-abc-5ac-4ab-20\\-a(bc+5c+4b+20)\\-a*c(b+5)+4(b+5)\\-a*(b+5)(c+4)[/tex]

The factor of the given expression is -a(b+5)(c+4)

What is factorization?

Factorization in maths is the process of breaking down a number or a mathematical object into smaller or simpler factors that can be multiplied together to get the original number or object

Given is an expression, –abc –5ac –4ab –20a, we need to factor it completely,

-abc -5ac-4ab-20

- a(bc +5c+4b+20)

- ac(b+5)+4(b+5)

- a(b+5) (c+4)

Hence, the factor of the given expression is -a(b+5)(c+4)

Learn more about factorization, click;

https://brainly.com/question/14549998

#SPJ2

0.000456 in scientific notation (Please answer fast this is on my final math exam!)

Answers

Answer:

0.000456 in scientific notation

= 4.56 × 10-4

Step-by-step explanation:

Can I have brainliest?

0.000456 in scientific notation is 4.56 × 10-4

Find the slope of the line represented by the data below x| 0 2 4 6 8
y|15 9 3 -3 -9
Slope=[?]

Answers

Answer:

it's answer is 10/-15.........

Which statement describes the system of equations? The system has infinitely many solutions. The system has no solution. The system has one solution The system has one solution

Answers

It’s B the system has no solution

I need help with these questions

Answers

Answer:

segment addition postulate

the second answer is true

Step-by-step explanation:

my teacher taught me this recently

What is the value of this expression?

−29−(−13÷35)

Answers

Answer:

-29 13/35

Step-by-step explanation:

Is it possible to draw a triangle whose sides have lengths 10.3 cm, 5.8 cm and 4.6 cm?Justify your answer.
(answer me fast kid)

Answers

Answer:

Yes it is possible

Step-by-step explanation:

let a = 10.3, b =5.8 , c= 4.6

a+b= 16.1>4.6=c

b+c=5.8+4.6=10.3>10.3=a

c+a=4.6+10.3=14.7>5.8=b.

5у2х 1.5y
If you could do this asap ty

Answers

Answer:

[tex]2.5y^{3}x[/tex]

Plug in missing values to make it a function…. Please help

Answers

Answer:

p = 5

Step-by-step explanation:

Judging from (0,0) and (10,-20) as given in the chart, the function is y = -2x.

Substituting that for the second row, you would get the equation -10 = -2x.

Simplifying, you get x = 5, so the value of p is 5.

Answer:

5

Step-by-step explanation:

First find the slope

m = ( y2-y1)/(x2-x1)

m = (-20-0)/(10-0)

   = -20/10

  = -2

We know the slope and have two points, (0,0) and (p,-10)

-2 = ( -10-0)/(p-0)

-2 = -10/p

Multiply each side by p

-2p = -10

Divide each side by -2

p = -10/-2

p = 5

Select the number line model that matches the expression | -6 - (-3)∣

Answers

-6 - (-3) remember ( a number in between ) this means positive number so that would mean that that equation would be 3
The absolute value means the value in side will be positive. - - or 2 negative signs give a positive number (cancel each other out). So it becomes -6 plus 3 which is -3. This would be the answer but absolute value signs mean that this value inside (-3) has to be positive.
The correct answer is a number line that shows 3.

divide 75 liters in the ratio 12 8 5

Answers

Answer:

According to the question,

[tex]12x + 8x + 5x = 75[/tex]

_____________________

[tex]12x + 8x + 5x = 75[/tex]

[tex]25x = 75[/tex]

[tex]x = \frac{75}{25} [/tex]

[tex]x = 3[/tex]

Now,

[tex]12x = 36[/tex]

[tex]8x = 24[/tex]

[tex]3x = 15[/tex]

So,

75 in the ratio of 12 : 8 : 5 is

36, 24 and 15

Answer:

36 : 24 : 15

Step-by-step explanation:

sum the parts of the ratio, 12 + 8 + 5 = 25 parts

Divide the quantity by 25 to find the value of one part of the ratio

75 l ÷ 25 = 3 l , then

12 parts = 12 × 3 = 36 l

8 parts = 8 × 3 = 24 l

5 parts = 5 × 3 = 15 l

8.3g of sugar is needed for every cake made. How much sugar is needed for 5 cakes?

Answers

Answer:

41.5g of sugar

Step-by-step explanation:

8.3 x 5

i need help with this question but keep f
getting decimals, it's not supposed to be a decimal for the answer. were solving systems by substitution

here's the question and will give brainy to someone who solves both

4x - 7y = 10
y = x - 7


x = 16 - 4y
3x + 4y = 8​

Answers

Answer:

1. y=18, x=25 2. y=5, x=-4

Step-by-step explanation:

For the first one, you have to find what x or y equals, and I chose x. x would equal y+7. Then I just plugged in x to the other equation and solved for y. After finding y, 18, I plugged it back into the first equation and got 18+7=25. I did the same steps for the 2nd one as well.

distributive property

Answers

Answer:

that's have no answer so sorry

Can you write out the question? Can’t see it in the picture.

Is f(x)=x^3-x symmetric about the origin

Answers

Answer:

-24 po

Step-by-step explanation:

thanks for the points

Please help

A

B


C

D

E

F

Answers

Answer: B. SAS or/and E. HL

Step-by-step explanation:

The two triangles both have a right angle of 90 degrees and two sides that are congruent so, SAS (side-angle-side). It can also be by HL since they both have a hypotenuse (the 2 lines) and one leg (the 1 line) that are congruent to each other.

what is the difference of 256,805+136,667

Answers

The difference is 120138 (if you are subtracting)
If you’re adding it’s 393472

Please help and no links;)

Answers

Answer:

3w + 8 = 2

Step-by-step explanation:

product of a number and 3 is w * 3

eight more than the above is 3w + 8

which is equal to 2

3w + 8 = 2

What is the distance between (-4,-8) and (2,3)?​

Answers

Answer:

Always computable as rightmost x value minus leftmost value: 4 - (-8) = 12

solve pls brainliest

Answers

Answer:

5/2

Step-by-step explanation:

please mark me brainiest

1/10 = 10%

a percent is

[tex] \frac{part}{whole} = \frac{x}{100} [/tex]

If u take 1/10, 10 is one tenth of 100 (10*10=100).

solve for x:
4x-14=-2x+24

Answers

Answer: 6 1/3

Step-by-step explanation:

4x-14 = -2x+24

4x = -2x+24 + 14  [Add 14 to both sides]

4x + 2x = 24 + 14  [Add 2x to both sides]

6x = 38                 {Combine like terms]

 x  = (19/3) or 6 1/3

There are 50 sheets of scrapbook paper in a pack, and 20% of them are striped. How many sheets of scrapbook paper are striped? Pick the model that represents the problem. How many sheets of scrapbook paper are striped?

Answers

Answer:

10 sheets of paper are striped

Step-by-step explanation: Make a proportional relationship.

20% as a fraction is 20/100

Make 50 into a fraction using a variable. For example, x/50

Cross multiply 20 and 50. That equals 1000.

Then divide 1000 by 100 and that equals 10. So 10 sheets of paper are striped.

Hope this helps!

The sides of a triangle are in the ratio 4:4:3.What kind of triangle is it

Answers

Answer:

Isosceles triangle. An Isosceles triangle is a triangle that has 2 equal sides and 2 equal angles

Step-by-step explanation:

Help I need a helping hand
A boat travels at a rate of 30 miles per hour for 3.5 hours. Let y be the distance, in miles, the boat travels for a given amount of time, x, in hours. This situation can be modeled by a linear function. What is the domain of the function?

Question 11 options:

0≤y≤30

0≤y≤3.5

0≤x≤3.5

0≤x≤30

Answers

Answer:

Step-by-step explanation:

Recall that distance = (rate)(time).  Here the rate is 30 mph and the time 3.5 hr.  The distance traveled is proportional to the time passing by.  The graph of the distance function is a straight line with slope equal to the "rate" named above:

d(x) = (30 mph)x

Since x (elapsed time) can't be negative in this situation, we write the domain as 0 ≤ x ≤ 3.5 hr.

name the coefficent 5x+10

Answers

Answer:

Coefficient is 5

Step-by-step explanation:

Coefficient means a numerical or constant quantity placed before and multiplying the variable in an algebraic expression.

Hope this is helpful.

Solve the following inequality.
-9 < 5 + 2.0 < -5
[?] < x <[
]

Answers

Step-by-step explanation:

you work with it like with regular equations :

-9 <= 5 + 2x <= -5

-14 <= 2x <= -10

-7 <= x <= -5

The length of a rectangle is (2x + 1). The width of the rectangle (x2+ 2x - 1). Which expression represents the area of the rectangle?

Answers

Answer:

Area = 2x³ + 5x² - 1

Step-by-step explanation:

Given the length of a rectangle, (2x + 1), and its width of (x² + 2x - 1):

The formula for solving the area of a rectangle is given by:

Area of a rectangle = Length × Width

In order to solve for the area of a rectangle, simply multiply the given length by the width.

length (L) = (2x + 1)

width (W) = (x² + 2x - 1)

A = L × W

A = (2x + 1)(x² + 2x - 1)

Distribute the binomial, (2x + 1), into the trinomial, (x² + 2x - 1):

A = 2x³ + 4x² - 2x + x² + 2x - 1

Combine like terms:

A = 2x³ + 5x² - 1

Therefore, the area of a rectangle is: 2x³ + 5x² - 1.

solve for c 11=-1-c/2 and have a bless day

Answers

c/2= -12
c=-24.
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Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers.
Brad and Laura are playing a board game. In the game, a player rolls two standard number cubes to move his or her game piece along
a path on the board. On the first three turns in the game, both number cubes land on six each turn.
The theoretical probability of rolling a six on both number cubes three times in a row is 1/?
(are/ are not)
Based on the probability of rolling a six on both number cubes three times in a row, Brad and Laura
likely using unfair number cubes.

Answers

Answer:

1/46,656 and Brad and Laura ARE like using unfair number cubes.

Step-by-step explanation:

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